Problem Statement

You are given N lines on the xy-plane. The i-th line (1 \le i \le N) passes through two distinct points (a_i, b_i) and (c_i, d_i). Specifically, (a_1, b_1, c_1, d_1) = (0, 0, 1, 0) and (a_2, b_2, c_2, d_2) = (0, 0, 0, 1). That is, the first line represents the x-axis, and the second line represents the y-axis.

Alice is on the xy-plane. She can perform the following operation any number of times (including zero):

Choose one of the N given lines. Alice moves to the position symmetric to her current position with respect to the chosen line.

Additionally, we define that point P is reachable from point S if the following condition is satisfied:

For any real number \varepsilon > 0, there exists a point Q such that the Euclidean distance between Q and P is at most \varepsilon, and Alice can move from S to Q in a finite number of operations.

Answer Q queries. For the i-th query (1 \le i \le Q), you are given integers X_i, Y_i, Z_i, W_i. Output Yes if (Z_i, W_i) is reachable from (X_i, Y_i). Otherwise, output No.

Solve the problem for T test cases.

Constraints

• All input values are integers.
• 1 \le T \le 100
• For each test case:
  • 2 \le N \le 2000
  • 1 \le Q \le 2000
  • -10^8 \le a_i, b_i, c_i, d_i \le 10^8 \ (1 \le i \le N)
  • (a_i, b_i) \neq (c_i, d_i)
  • (a_1, b_1, c_1, d_1) = (0, 0, 1, 0)
  • (a_2, b_2, c_2, d_2) = (0, 0, 0, 1)
  • All given lines are distinct.
  • -10^8 \le X_i, Y_i, Z_i, W_i \le 10^8 \ (1 \le i \le Q)

Sample Input 1

2
3
0 0 1 0
0 0 0 1
0 2 2 0
4
1 0 2 3
1 -2 -1 2
1 1 -1 0
3 3 3 3
3
0 0 1 0
0 0 0 1
-2 1 2 3
2
2 1 -1 5
-1 -1 3 3

Sample Output 1

Yes
Yes
No
Yes
Yes
Yes

Let us explain the first test case. For the first query, Alice can use the second and third lines in sequence to move (1, 0) \to (-1, 0) \to (2, 3). Thus, (2, 3) is reachable from (1, 0). Note that for the fourth query, if (X_i, Y_i) = (Z_i, W_i), the destination is always reachable.

Now let us explain the second test case. For the first query, Alice can use the first and third lines in sequence to move (2, 1) \to (2, -1) \to \left(-\frac{6}{5}, \frac{27}{5}\right). The distance between (-1, 5) and \left(-\frac{6}{5}, \frac{27}{5}\right) is \frac{1}{\sqrt{5}}. This means that for \varepsilon \ge \frac{1}{\sqrt{5}}, Alice can find a point Q that satisfies the "reachable" condition. Moreover, for any \varepsilon > 0, Alice can find such a point Q. As a result, (2, 1) is reachable from (-1, 5).